On Maximizing a Sum of Ratios

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Abstract
The problem of maximizing the sum of m concave-convex fractional functions on a convex set is shown to be equivalent to the one whose objective function f is the sum of m linear fractional functions defined on a suitable convex set; successively, f is transformed into the sum of one linear function and (m — 1) linear fractional functions. As a special case, the problem of maximizing the sum of two linear fractional functions subject to linear constraints is considered. Theoretical properties are studied and an algorithm converging in a finite number of iterations is proposed.

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